System and method of quantum computing using three-state representation of a qubit

ABSTRACT

A method (and structure) of quantum computing. Two independent magnitudes of a three-state physical (quantum) system are set to simultaneously store two real, independent numbers as a qubit. The three-state physical (quantum) system has a first energy level, a second energy level, and a third energy level capable of being degenerate with respect to one another, thereby forming basis states for the qubit.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention generally relates to a qubit (quantum bit). Morespecifically, a qubit is represented by a three-state physical system.

2. Description of the Related Art

The computing power of microprocessors has been doubling every 18 monthsover the last three decades. This doubling of power has been achieved byreducing the physical size of the basic computing unit, i.e., atransistor. Some of the dimensions of the transistor are currentlyapproaching atomic sizes. At such small dimensions classical physicsbreaks down and this break down has resulted in a number of problemsrelated to providing computing capability.

The most prevalent problem is the increase in the power requirements forthe microprocessor due to a quantum mechanical effect called tunneling,which causes the loss of power. This problem of loss of power isexpected to get worse as the dimensions of the transistor are furtherreduced.

Known Solution

In order to remediate the problem of the breakdown of classical physicsat such small dimensions, which thereby translates to the consequentloss of power in a transistor, computers based on quantum physics havebeen proposed within the industry. Such computers are now known as“quantum computers”.

Quantum computers employ non-intuitive properties of quantum physics.Such properties are not fully understood but can yield extremelypowerful computers for the future. An example of such non-intuitiveproperties in quantum physics is superposition. The principle ofsuperposition implies that a particle can be at two places at the sametime. This is in contrast to classical physics, which limits a particleto one place at a given time.

Using this property, scientists have defined a basic computationalquantity called the “qubit” (i.e., quantum bit). The qubit has theproperty that it can store two numbers at the same time, unlike aclassical bit, which can store only one number at any given point intime. This property of storing two numbers at the same time in a qubitleads to extremely powerful computers in terms of speed, parallelprocessing, memory, and physical size of the computer.

It has been shown that these quantum computers can solve computationallycomplex problems, which are considered intractable using theconventional modern computers. An example of such computationallyintensive problem is the factorization of a large number into its primefactors. Such a factorization problem is the key ingredient in encodingof the data for protection from unauthorized reading and use.

Issue Surrounding the Known Solution

Up to now, qubits have been represented by two-state physical systems.Examples of such two state physical systems are a nuclear spin of ahydrogen atom, a photon with two polarizations, a trapped neutral atomwith two states, and a trapped ion with two states. In each of thesetwo-state physical systems, the state can be represented as thesuperposition of the two states. In order to describe such asuperposition state, two real numbers, one phase and one magnitude, areneeded.

In other words, such a superposition state can store two numbers at thesame time and thus represent a qubit.

However, in the conventional representations of a qubit, only one ofthese two numbers, the magnitude, can be read out easily. It isextremely difficult to read out the second number, namely the phase.Thus, in all of two-state systems studied so far, only in one system(e.g., the trapped ion) has there been demonstrated a control over bothnumbers. But in this system, scalability to computing devices containingmore than two or three qubits has been a huge challenge.

Therefore, a need continues to exist for a design of a qubit having boththe capability of storing two numbers and easily reading out two storednumbers while maintaining the property of scalability.

SUMMARY OF THE INVENTION

In view of the foregoing, and other, exemplary problems, drawbacks, anddisadvantages of the conventional systems, it is an exemplary feature ofthe present invention to provide a structure (and method) in which athree-state system is employed to represent a qubit.

Such three-state physical system has two independent magnitudes that canrepresent a qubit. Since the magnitudes are related to probabilities forthe system to be in one of the three possible states, they can easily beread out. In this scheme of physical representation of a qubit, the twoindependent phases of the three state systems are not used at all.Therefore, the question of not being able to read out information storedin such phases does not arise.

Therefore, in a first exemplary aspect of the present invention, toachieve the above features and objects, described herein is a method ofquantum computing including setting two independent magnitudes of athree-state physical (quantum) system to simultaneously store two real,independent numbers, the three-state physical (quantum) systemcomprising a first energy level, a second energy level, and a thirdenergy level capable of being degenerate with respect to one another,and thereby considered as forming basis states for the qubit.

In a second exemplary aspect of the present invention, also describedherein is a quantum bit (qubit) simultaneously storing two real,independent numbers, the qubit comprising a three-state physical(quantum) system including a first energy level, a second energy level,and a third energy level, where the first energy level, the secondenergy level, and the third energy level are capable of being degeneratewith respect to one another, the first energy level, second energylevel, and third energy level are considered to form basis states forthe qubit, and wherein two real, independent numbers of the qubit arestored as two independent magnitudes of the three-state physical(quantum) system and two independent phases of the three-state physical(quantum) system are not used for storing the two real, independentnumbers of the qubit.

In a third exemplary aspect of the present invention, also describedherein is a method of storing information into a qubit (quantum bit),including applying a radio frequency (RF) pulse having a pulse widthpredetermined to cause two magnitudes in a three-state physical systemto simultaneously assume predetermined values due to a superpositioneffect in the three-state physical system, wherein the three-statephysical system includes a first energy level, a second energy level,and a third energy level capable of being degenerate with respect to oneanother, thereby considered as forming basis states for the qubit.

In a fourth exemplary aspect of the present invention, also describedherein is a method of reading information stored in a qubit, includingtransmitting radio frequency (RF) energy in a scanning manner over apredetermined RF frequency range to a sample of material having athree-state physical system; receiving a spectral response of the sampleof material resultant from the scanning; and determining an informationcontent of the sample of material from the received spectral response,wherein the three-state physical system includes a first energy level, asecond energy level, and a third energy level capable of beingdegenerate with respect to one another, thereby considered as formingbasis states for the qubit.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other features, aspects and advantages will be betterunderstood from the following detailed description of preferredembodiments of the invention, with reference to the drawings, in which:

FIG. 1 shows a typical set up 100 for a continuous wave spectrometerthat can be used to obtain the RF spectrum that shows two peaks of athree-state system;

FIG. 2 shows a typical set up 200 for obtaining an absorption spectrumof a three-state system;

FIG. 3 shows a typical waveform 300 as would be used for storinginformation into a three-state system;

FIG. 4 shows an exemplary absorption spectrum 400 having a singleabsorption peak 401, for a two-state system;

FIG. 5 exemplarily shows an absorption spectrum 500 having the two peaks501, 502 of a three-state system, as used in the present invention;

FIG. 6 exemplarily shows the two-energy split 600 of a two-state systemwhen a small static magnetic field is applied; and

FIG. 7 exemplarily shows the three-energy split 700 of a three-statesystem upon application of a small static magnetic field.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS OF THE INVENTION

Referring now to the drawings, and more particularly to FIGS. 1-7,exemplary embodiments of the method and structures according to thepresent invention will now be explained.

The following summarizes novelty of the present invention:

-   -   1. Three-state representation of a qubit in the certain way        described above is new. Normally the qubit is represented by a        two-state system. With this invention the qubit is represented        as the combination of qubit and three-state.    -   2. Representing the qubit with a Spin S=1 system is new.    -   3. Representing the qubit with the nuclear spin of a        Deuterium (D) atom is new.    -   4. Representing the qubit with the nuclear spin of either Copper        (Cu), Silver (Ag), Gold (Au), Lithium (Li) or Nitrogen (N) atom        is new. All these nuclei have a spin S=1.    -   5. Use of NMR (Nuclear Magnetic Resonance) to make measurements        of the numbers stored in the nuclear spin of the Deuterium,        Copper, Silver, Gold, Lithium or Nitrogen (N) atom is new (for        purpose of representing a qubit).    -   6. Use of three-state atom as representing a qubit is new.    -   7. Use of three-state atoms such as Boron (B), Aluminum (Al),        Gallium (Ga), Indium (In) or Thalium (Tl) to represent a qubit        is new.    -   8. Use of atomic spectroscopy, in particular absorption atomic        spectroscopy, to measure the two numbers stored in a three-state        atom or ion is new.    -   9. Use of a three-state ion as representing a qubit is new.        Examples of such ions include C⁺¹, Si⁺¹, Ge⁺¹, Sn⁺¹, and Pb⁺¹.        -   No alternate known solutions exist at this point in time.        -   An “atom” or “ion”, in the context of describing the present            invention, means a sample of that material containing atoms            or ions that are substantially identical for so that a            substantially uniform measurement of a sample theoretically            represents the measurement of a single atom or ion.            Currently, sample with atoms or ions can be prepared in            identical states only at very low temperatures. The actual            number of atoms or ions necessary to measurably achieve            described effects is expected to become smaller over time,            including an ultimate possibility of being able to utilize a            single atom or ion to represent a qubit, similar to the            concept that transistor technology is approaching the            theoretical limit of using a single atom or molecule.

As summarized above, according to the present invention, a qubit will berepresented by a three-physical-state system. In such a three-statesystem, the general state of the system can be specified by specifyingtwo independent magnitudes and two independent phases.

In the solution described in this disclosure, the two independent phaseswould not be used for storing or retrieving information. The twoindependent magnitudes are enough to represent a qubit. These twoindependent magnitudes are easy to read out since they correspond toprobabilities of the system being in one of the three possible states.In other words, they correspond to the classical variables.

The present invention can be implemented in a number of different ways.Some of the three physical state systems that can be used are:

-   -   1. A nuclear spin with a spin value of 1;    -   2. An atom or a molecule with three possible physical states;        and    -   3. An ion with three possible physical states.

A concrete example of a nuclear spin with a spin value of 1 is theDeuterium nucleus. Deuterium is an isotope of Hydrogen and its nucleusconsists of a proton and a neutron. Both the proton and neutron have aspin of ½, producing a net spin of 1 for the nucleus. Such a nuclearspin has three states, commonly represented by 1, 0, −1.

In order to read out the stored numbers, standard NMR (Nuclear MagneticResonance) techniques can be employed. First, a static magnetic field isapplied. This magnetic field splits the three states into threedifferent energy states. After applying the static magnetic field, aradio frequency field is applied with a variable frequency so as to scanacross a predetermined frequency range. This application of the radiofrequency field will show two peaks at two different energies (orfrequencies). From the heights of the two peaks, the two stored numberscan be easily obtained.

The simplest method of obtaining the spectrum is referred to as thecontinuous wave (CW) method. A typical CW-spectrometer is shown in theFIG. 1. A solution of the sample in a uniform 5 mm glass tube isoriented between the poles of a powerful magnet, and is spun to averageany magnetic field variations, as well as tube imperfections. Radiofrequency (rf) radiation of appropriate energy is broadcast into thesample from an antenna coil 103. A receiver coil 104 surrounds thesample tube, and emission of absorbed rf energy is monitored bydedicated electronic devices 105,106, that could include a computer withcontrol instructions for the transmission and reception of rf signals.An NMR spectrum is acquired by varying or sweeping the magnetic fieldover a small range while observing the rf signal from the sample. Anequally effective technique is to vary the frequency of the rf radiationwhile holding the external field constant.

Similar techniques are also available for other three state systems suchas a three-state atom/molecule or a three-state ion. For example, incase of atoms, atomic spectroscopy can be employed to observe theabsorption peaks. A particular form of atomic spectroscopy is calledabsortion spectroscopy.

As exemplarily demonstrated by the experimental setup 200 shown in FIG.2, absorption spectroscopy is a technique in which the power of a beamof light measured before and after interaction with a sample 201 iscompared. When performed with a tunable laser diode 202 as a source oflight, it is often referred to as Tunable Diode Laser AbsortionSpectrocopy (TDLAS).

In FIG. 2, a light beam from a laser diode 202 is first focused at asplitter (half-silvered minor) 203, which splits the beam into twoparts. The first part of the light bean is passed through the sample 201on in its way to a signal photo diode 204. The sample 201 absorbs someof the light. The second part of the light beam is used as a referencefor comparison purposes. The two parts of the beam is fed into a logdevice 205 as two inputs, which performs the comparison and produces anabsorption spectrum.

Storing Information

In the exemplary nuclear Spin S=1 three-state system, the two numberscan be stored by preparing the superposition state, which corresponds tothe two numbers of the qubit. This state preparation of the staterequires the following two steps:

-   -   1. First, a static magnetic field is applied, which will align        the nuclear Spin S parallel to the magnetic field.    -   2. Second, an RF (radio frequency) pulse of for a short duration        is applied, as shown in FIG. 3. This application of the RF pulse        301 will rotate the nuclear spin. The resulting final state, in        general, will be a superposition of the three state levels of        the nuclear Spin S=1. A specific superposition state can be        generated by controlling the width of the RF pulse, thereby        setting the system to simultaneously store two numbers, as        further explained below.        Determination (Roshen-Vaidya) Test for a Three State System        Presence for the New Solution        Summary of Test

There is one test which can be used to determine if the three-statesystem is being used instead of a two-state system to represent a qubit.In this method, first, one applies a small static magnetic field whichsplits the states into separate energy states. Then, one applies atime-varying electromagnetic wave signal whose frequency can be varied.

In case of two-state system the electromagnetic wave shows a singleabsorption peak (see FIG. 4), while in case of a three-state system, twopeaks at two different frequencies are observed in the absorptionspectrum (see FIG. 5). Thus, this test is clearly able to distinguishbetween two- and three-state representations of qubits.

New Solution—Details of the Test

The following steps are involved in this test:

-   -   1. First one applies a small static magnetic field. The result        of the application of this magnetic field is that the states,        which are equal in energy in the absence of the magnetic field,        are split in energy. For example in the case of two-states, the        situation is shown in FIG. 6, which shows two states being split        in energy by an amount ΔE_(o). Similarly, in the case of        three-state system the three states split into three energy        levels as shown in FIG. 7.    -   2. In the second step, a variable-frequency electromagnetic wave        is applied to the system and the absorption of the        electromagnetic waves by the system is monitored. This        absorption of the electromagnetic occurs because the system is        able to make a transition from a lower energy state to a higher        energy state. The outcome of absorption monitoring is different        for the two state systems and the three state systems:        -   In the case of two-state system only one absorption peak is            observed as shown in the FIG. 4. This is made clear by            considering FIG. 6, which shows this transition by a dotted            arrow. It is clear from FIG. 6 that only one transition from            lower energy state to higher energy state is possible.        -   In the case of three state systems two distinct absorption            peaks are observed as shown in FIG. 5. This observation of            two peaks can be explained on the bases of FIG. 7, which            shows that there are three energy states. In principle three            absorption peaks should be observed, however, two of these            two peaks occurs at the same frequency because the change            (delta) of energies for these two transitions are equal.            Thus two of the three peaks superimpose on each other and            only two distinct peaks are observed.            The Present Invention Compared with Previous Qubit            Representations

There are two other previously known three-state related quantities.These older quantities are separate and distinguishable from the newQubit with three-state representation that is presented in the presentinvention. For clarity purpose, we will refer to the new Qubit withthree state representation as WS-Qubit.

The following table summarizes the differences of this new WS-Qubit withthe two other previously known three-state related quantities. Pleasenote the words “and” and “or” in the second column. Which of these twowords is used makes a big difference in terms of how many total numberscan be stored at a given time as shown in the third column.

The comparison of the entries in the second and third columns shows thatWS-Qubit is clearly different and distinguishable from the twopreviously known, three-state quantities, namely Trit and Qutrit.

Possible numbers Total numbers stored Ouantitv can be stored at a giventime WS-Qubit: Qubit with 0 and 1 2 three-state representation 0.1 or 21 Classical Tri-state bit (a.k.a Trit) Qutrit (Quantum tri-state 0, 1,3, and 4 4 quantity) (possibly more)

Amin et al. have previously considered three-state systems for buildingquantum gates, which are needed for quantum logic. However, their qubitrepresentation employs only two out of three states. They represent thequbit in the conventional way by using the superposition of these twostates as:|ψ

=α|0

+β|1

where |0

and |1

are the two degenerate states and α and β are called probabilityamplitudes. α and β are both complex numbers, each one having amagnitude (a real number) and a phase (also a real number). The twomagnitudes |α| and |β| are related by the following normalizationcondition:|α|²+|β|²=1

This normalization condition means that only one of these two magnitudesis independent and one is forced to use one of the phases (the relativephase) to fully represent the two numbers of the qubit.

In contrast to what is described in Amin et al.'s patent, the presentinvention uses three states to represent the qubit as follows:|ψ

=α|0

+β|1

+γ|2

where α, β, and γ are three probability amplitudes and |0

, |1

, and |2

are the three degenerate states of a three-state system. α, β, and γ arethree complex numbers called probability amplitudes for the three-statesystems. Each of these three complex numbers has a magnitude (a realnumber) and a phase (also a real number). The magnitudes are related bythe following normalization condition:|α|²+|β|²+|γ|²=1

This normalization condition means that for the three-staterepresentation two independent magnitudes are available to represent twonumbers of a qubit. In the present invention we use only these twoindependent magnitudes as representing the two numbers of a qubit. Inview of the above descriptions of the comparisons of the conventionalconcepts and implementations of a “qubit”, the present invention couldalso appropriately be described as providing a “modified qubit” relativeto qubits currently known in the art.

From the foregoing description, it should be clear to one havingordinary skill in the art that the present invention would make it easyto retrieve the information stored in a qubit. More specifically, itwill allow both of the numbers stored to be measured and retrieved withease. The present invention also describes new methods for retrievingthe information stored in this new qubit, such as NMR spectroscopy andatomic spectroscopy. The present invention also introduces a new conceptof using three-state systems that can be used to represent a qubit.These new three-state systems include nuclear spins each having a valueof 1 and many more there-state atoms and ions.

It is expected that use of these three-state systems would acceleratethe development of practical quantum computers. Quantum computers haveenormous power in terms of speed, memory, and size compared to moderncomputers which are based on classical physics.

While the invention has been described in terms of exemplaryembodiments, those skilled in the art will recognize that the inventioncan be practiced with modification within the spirit and scope of theappended claims.

Further, it is noted that, Applicants' intent is to encompassequivalents of all claim elements, even if amended later duringprosecution.

1. A method comprising: setting two independent magnitudes of athree-state quantum system to simultaneously store two real, independentnumbers as a qubit, said three-state quantum system comprising a firstenergy level, a second energy level, and a third energy level capable ofbeing degenerate with respect to one another and thereby considered asforming basis states for said qubit.
 2. The method of claim 1, whereintwo independent phases of the three-state quantum system are not usedfor storing the two real, independent numbers of the qubit.
 3. Themethod of claim 2, further comprising: measuring stores values of saidtwo independent magnitudes, thereby determining said two number beingsimultaneously stored in said qubit.
 4. The method of claim 1, whereinsaid three-state quantum system comprises a nuclear spin with a spinvalue of
 1. 5. The method of claim 4, wherein said nuclear spin belongsto an atom, which comprises a part of a molecule.
 6. The method of claim5, wherein said atom or said molecule is dissolved in a liquid or aliquid-crystal.
 7. The method of claim 5, wherein said atom or saidmolecule is in a form of a gas.
 8. The method of claim 5, wherein saidatom or said molecule is in a form of a liquid.
 9. The method of claim5, wherein said atom or said molecule is in a form of a solid.
 10. Themethod of claim 4, wherein said three-state quantum system comprises aDeuterium nucleus, having a proton and a neutron, both the proton andneutron having a spin of ½, producing a net spin of one 1 for theDeuterium nucleus, the nuclear spin thereby having three states,represented as 1, 0, −1.
 11. The method of claim 4, wherein saidthree-state quantum system comprises a nucleus of an atom of one of:Copper (Cu); Silver (Ag); Gold (Au); Lithium (Li); and Nitrogen (N). 12.The method of claim 1, wherein said three-state quantum system comprisesan atom or a molecule with three-physical states.
 13. The method ofclaim 12, wherein said three-state quantum system comprises athree-state atom, comprising one of: Boron (B); Aluminum (Al); Gallium(Ga); Indium (In); and Thalium (Tl).
 14. The method of claim 1, whereinsaid three-state quantum system comprises an ion with three-physicalstates.
 15. The method of claim 14, wherein said three-state quantumsystem comprising a three-state ion comprises one of: C.sup.+1,Si.sup.+1, Ge.sup.+1, Sn.sup.+1, and Pb.sup.+1.
 16. A quantum bit(qubit) simultaneously storing two real, independent numbers, said qubitcomprising: a three-state quantum system including a first energy level,a second energy level, and a third energy level, said first energylevel, said second energy level, and said third energy level capable ofbeing degenerate with respect to one another, said first energy level,said second energy level, and said third energy level considered to formbasis states for said qubit, wherein two real, independent numbers ofsaid qubit are stored as two independent magnitudes of said three-statequantum system and two independent phases of the three-state quantumsystem are not used for storing the two real, independent numbers of thequbit.
 17. The qubit of claim 16, wherein said two independentmagnitudes correspond to heights of two peaks in a frequency spectrum ofsaid three-state quantum system.